End Users reply to e-mails

If I send an e-mail response to a user's support request who does not have access to lighthouse and cc the e-mail address for that ticket and the user does a reply all with additional information regarding the initial request, will their responses be captured in lighthouse?

OK so now I know the end user would have to be setup as a "user" in lighthouse, correct? Is there any other option for allowing a non-lighthouse user to submit updates to an existing lighthouse ticket?